Rigidity and Non-Rigidity of $\mathbb{H}^n/\mathbb{Z}^{n-2}$ with Scalar Curvature Bounded from Below
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Published:2023-11-01
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ISSN:1815-0659
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Container-title:Symmetry, Integrability and Geometry: Methods and Applications
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language:
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Short-container-title:SIGMA
Author:
Hao Tianze, ,Hu Yuhao,Liu Peng,Shi Yuguang, , ,
Abstract
We show that the hyperbolic manifold $\mathbb{H}^n/\mathbb{Z}^{n-2}$ is not rigid under all compactly supported deformations that preserve the scalar curvature lower bound $-n(n-1)$, and that it is rigid under deformations that are further constrained by certain topological conditions. In addition, we prove two related splitting results.
Publisher
SIGMA (Symmetry, Integrability and Geometry: Methods and Application)
Subject
Geometry and Topology,Mathematical Physics,Analysis